Aztecs, Mayans, & Incas are pretty knew on the scene, forming in the late to high middle ages, the Aztecs only coming to power about a century before they fell to Cortes. Lots of carnage candy though, some of it's actually really sick.
the Romans, Celts, & Greeks are more classical than ancient, but that depends on how technical you want to get. The Celts are cool for how their respective governments worked, their kings were all but elected. The Greeks just bicker with one another and then get huge, then fall, & the Romans will shed light on our current problems, especially once the Republic falls & the Empire takes it's place
The Indus Valley Civilizations are fascinating, especially since the boxing Day Tsunami, historically they are the contenders for the crown of the world's oldest civilization as well as longest perpetual culture, it's under intense debate at the moment.
Catal Huyuk is an archeological site, not really a civilization in on itself. But extremely old in that's it's neolithic (New Stone Age) the down side is that unless you're studying archeology, there won't be finding much material on it, unless you like pot shards, fertility gods, & arrow heads
By Crete I believe you mean the Minoan Civilization, who are contenders for the possible sit of ancient Atlantis' & Plato's famous civilization
Japan just takes off, but like Egypt, after a while, just becomes static, repetitive, & very long.
Yes, Egypt is an ancient civilization, BUT, at the start it's awesome to study, then boring & one Pharaoh after another that doesn't really do anything, then they get invaded, things get interesting as they rebuild, expand, then become static again for a very long & very boring series of centuries.
The Phoenicians are fascinating, especially if you like the idea of ancient trade routes & exploration, there's a lot more to them of course, but they are the mega-explorers of the ancient world, & that is really cool
For Society & Environment, we have to do a major assignment on an ancient civilisation. We have to choose out of these... which one do you think is the most interesting?